Fmcw radar sensor including synchronized high frequency components

ABSTRACT

A method for encoding and storing digital data, which include a plurality of real values, in a signal processing unit of a radar sensor in which at least one real value r in an exponential representation in the form r=m·b−k is stored, where m is a digital mantissa having a length p, b is a base, and k is a positive number that is encoded as a digital number having a length q. An exponential representation with b&gt;2 is used for the compressed storage of the values r.

CROSS REFERENCE

The present application claims the benefit under 35 U.S.C. § 119 ofGerman Patent Application No. DE 102019213621.4 filed on Sep. 9, 2019,and German Patent Application No. DE 102019215191.4 filed on Oct. 2,2019, both of which are incorporated herein by reference in theirentireties.

FIELD

The present invention relates to a method for encoding and storingdigital data, which include a plurality of real values, in a signalprocessing unit of a radar sensor in which at least one real value r inan exponential representation in the form

r=m·b ^(−k)

is stored, where m is a digital mantissa having a length p, b is aninteger base, and k is a positive number that is encoded as a digitalnumber having a length q.

In particular, the present invention relates to the encoding and storingof digital data in a radar sensor for motor vehicles.

BACKGROUND INFORMATION

In radar sensors for motor vehicles, the transmitted radar signal isgenerally a cyclically frequency-modulated signal, for example asequence of frequency ramps emitted in succession, or also a sequence ofso-called orthogonal frequency-division multiplexing (OFDM) symbols. Thesignals received from the located objects are downmixed into alow-frequency baseband, and after preamplification are digitized withthe aid of an analog/digital converter. Thus, for each modulation cyclea time signal in the form of a vector x(n) is obtained, whose componentsare real or complex, depending on the demodulation method used, and aredigitally represented. The number of components, i.e., the dimension ofthe vector, corresponds to the number of measuring points in time atwhich the signal is evaluated within the modulation cycle.

Vector x(n) may be converted via at least one Fourier transform (FFT,for example) into a vector V(k) whose complex components indicate theamplitude and phase of the received signal as a function of frequency k.The dimension of this vector corresponds to the number of frequency binson the frequency axis, and thus determines the frequency resolution.

In many conventional radar systems for motor vehicles, each modulationcycle includes a plurality of successive frequency ramps or OFDM symbolsthat may be counted with the aid of an index y. In this case, atwo-dimensional matrix may be formed by a further fast Fourier transformof the vectors V_(y)(k) via index y. Each cell of this matrix thenrepresents a combination of a distance d and a relative velocity v, andthe cells, in which the value obtained via the two-dimensional FFTassume a maximum, represent objects that have been located at distance dand with relative velocity v.

When the radar sensor includes an array with multiple receivingantennas, and the signals of the receiving antennas are evaluated inseparate reception channels, the azimuth angle and/or elevation angle atwhich the object is located may thus also be determined based on theamplitude and phase relationships of the signals that are obtained inthe various channels for the same object.

With increasing demands on the distance resolution and angularresolution of the radar sensor, the number of reception channelsincreases, and within each reception channel the dimension of vectorsx(n) and V(k) to be processed likewise increases, so that a considerabledata volume is to be processed within each modulation cycle. Thisrequires not only fast processors, but also a high memory capacity forthe temporary storage of the digital input values as well as theintermediate results obtained in each processing step. The increaseddemand for memory capacity results in increased chip size and highercosts, as well as greater energy requirements.

According to ANSI/IEEE Standard 754-1985, digital representations ofreal numbers are stored in the form r=m·2^(−k). The memory requirementsfor each real number are then specified by the sum of length p ofmantissa m and length q of exponent k. The representation of a complexnumber requires two real numbers, for example a real part and animaginary part.

U.S. Pat. No. 9,541,637 B2 and PCT Application No. WO 2015/185058 A1describe methods with which memory requirements are to be kept withinlimits by data compression.

SUMMARY

An object of the present invention is to provide a method with which thememory requirements may be further reduced, or for a given memory space,the location accuracy may be improved.

This object may be achieved according to an example embodiment of thepresent invention with a method in which an exponential representationwith b>2 is used for the compressed storage of the values.

As the result of using a larger integer base instead of the standardbase b=2, for a given total length of the mantissa and of the exponent ahigher resolution may be achieved for a significant portion of thevalues to be stored. Conversely, this means that for given requirementsfor the resolution, the length of the mantissa and/or of the exponentmay be reduced, and memory space is thus saved.

Advantageous embodiments and refinements of the present invention aredescribed herein.

In one advantageous specific embodiment, base b used is a power of two,for example b=4 or b=8. The conversion of the exponential representationfrom one base (b=2, for example) to another (b=4, for example) may thenbe carried out very easily, and requires very little additionalcomputing time. Optionally, it is also possible to generate the valuesin the exponential representation during the digitization in theanalog/digital converter, with b<2.

According to one advantageous refinement of the present invention, thevalues are transformed into an exponential representation in the form

r=m*·b ^(−f(k)),

where m* is the mantissa and f is a function of k that is selected frommultiple functions, and the selection of function f takes place based ona value distribution of the values to be stored.

Depending on the value distribution of the values to be stored, certainlower powers of b⁻¹ may not be necessary at all in the exponentialrepresentation. Function f may then be selected in such a way thatinstead of these unnecessary powers, higher powers that allow a higherresolution appear in the exponential representation. Digital number khaving length q is then used to encode, instead of the 2^(q) lowestpowers of b⁻¹, another, more suitable selection of powers in order toachieve a higher resolution without additional memory requirements.

The selection of function f may take place before initial start-up ofthe radar sensor. The selection criterion is then the probable valuedistribution of the values to be stored, which are most likely withregard to the properties, operating conditions, and tasks of the radarsensor.

However, the selection of function f may also be dynamically variedduring operation of the radar sensor, for example when there is a changein the requirement profile of the radar sensor, or optionally also basedon a random or continuous statistical analysis of the value distributionof the data to be stored.

Exemplary embodiments are explained in greater detail below withreference to the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a simplified circuit diagram of a radar sensor to which thepresent invention may be applied.

FIG. 2 shows a block diagram of a digital signal processing unit in theradar sensor according to FIG. 1.

FIG. 3 shows examples of the encoding of digital values in a standardformat.

FIGS. 4 through 6 show examples of the encoding of digital valuesaccording to a first exemplary embodiment of the present invention.

FIG. 7 shows a memory architecture for an encoding method according to afurther exemplary embodiment of the present invention.

FIGS. 8 through 10 show examples of the encoding of data according tothe method according to the second exemplary embodiment of the presentinvention.

FIG. 11 shows a diagram for explaining one modification of the methodaccording to FIGS. 8 through 10.

FIGS. 12 and 13 show histograms for explaining a further variant of themethod according to the second exemplary embodiment of the presentinvention.

FIG. 14 shows a block diagram of a signal processing stage for themethod according to the second exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 shows by way of example an FMCW radar sensor that includes atransceiver 10 with four antenna elements 12, 14, 16, 18, which togetherform a planar group antenna. The radar sensor is installed in the motorvehicle in such a way that antenna elements 12 through 18 are adjacentlysituated at the same height, so that a certain angular resolutioncapability of the radar sensor in the horizontal (in the azimuth) isachieved.

A high-frequency portion 20 for controlling the antenna elements isformed, for example, by one or multiple monolithic microwave integratedcircuits (MMICs), and includes an oscillator 22 that feeds atransmission signal into the individual antenna elements. The frequencyof the transmission signal is periodically modulated in the form of asequence of rising and/or falling frequency ramps. For example, eachmodulation cycle includes a sequence of so-called “rapid chirps,” i.e.,frequency ramps having the same slope, and each with a certain frequencyshift relative to one another. The radar echoes received from antennaelements 12 through 18 are decoupled in each case with the aid of acirculator 24 and supplied to a mixer 26, where they are mixed with thetransmission signal delivered by oscillator 22. In this way, a basebandsignal b1, b2, b3, b4, which is supplied to an electronic control andevaluation device 28, is obtained for each of the antenna elements.

Control and evaluation device 28 contains a four-channel analog/digitalconverter 30 which digitizes and records baseband signals b1 through b4obtained from the four antenna elements. The digital time signals thusobtained are then further processed channel by channel in a signalprocessing unit 32. For example, the time signals for each ramp areconverted via a fast Fourier transform into spectra, which then undergoa further Fourier transform via the ramp index. A two-dimensionalspectrum is thus obtained, from which distances d and relativevelocities v of located objects may be read off.

The values obtained via the Fourier transforms are complex numbers thatindicate the amplitudes and the phases of the received signals. Sincethe amplitude and phase relationships of the signals, which are receivedin the various reception channels from the same object, are a functionof the azimuth angle of the object in question, azimuth angle θ of theobjects may also be determined with a certain accuracy in an angleestimation module 34.

Maint components of signal processing unit 32 are illustrated as a blockdiagram in FIG. 2. The signal processing unit includes an input stage 36which accepts the digital data from analog/digital converter 30. Thedata are compressed in a compression stage 38 according to a method thatis explained in greater detail below. The data are then stored incompressed form in a memory 40. When the data are to be furtherprocessed, they are decompressed in a decompression stage 42 and thenfurther processed in a processing stage 44.

Signal processing unit 32 may also include multiple interlinkedprocessing stages 44, for example two FFT stages for a two-dimensionalFourier transform. The processing results of the first stage are thenrecompressed and stored in a further memory, which the downstreamprocessing stage then accesses via a further decompression stage. Incertain applications, processing stage 44 or a downstream processingstage may also be designed in such a way that it may directly processthe compressed data when they are stored in memory 40. Decompressionstage 42 is then bypassed, or forwards the data unchanged. It islikewise possible for a processing stage to change the compressed datadirectly in memory 40. The downstream processing stage then accessessame memory 40.

According to the IEEE 754-1985 standard, real values are encoded andstored in an exponential representation in the form r=m·b^(−k), whereb=2, m is a mantissa having a length p of 8 bits, for example, and k isa positive integer having a length q of 3 bits, for example. FIG. 3shows the digitization of a decimal number 0.8408203125 as an example.In binary fixed-point representation, this number is represented by thebit sequence 01101011101, which has a length of 11 bits. Above this bitsequence, the values of the associated binary digits are indicated asnegative powers of two in FIG. 3. The most significant bit has the value2°, the next bit has the value 2⁻¹, etc.

A table 46 in FIG. 3 illustrates the conversion of this fixed-pointnumber into the standard-exponential representation, with p=8, q=3, andbase b=2. Since exponent k has length q=3, k may assume values from 0 to7. Accordingly, table 46 includes eight rows. Since the mantissa haslength p=8, in the conversion to the exponential representation thethree least significant bits of the original bit sequence must bedropped. The eight-digit mantissa is entered into the row in table 46which (for positive numbers) is situated one digit left of the first bitof the original 11-bit sequence that is different from 0, thus, in rowk=0 in the present example. The stored value is thus to be interpretedas

r=m ₀·2⁻⁰ +m ₁·2⁻¹ + . . . +m ₇·2⁻⁷,

where m_(i) (i=0 to 7) is the ith digit of mantissa m.

In the present example, the mantissa is indicated in the two'scomplement format. In this format, for positive numbers the mostsignificant bit (at the left end of the sequence) must be equal to 0,while for negative numbers the most significant bit must be equal to 1.When the original bit sequence contains more than one leading 0, theleading zeroes except for the last one may be omitted, and for eachomitted 0, exponent k is increased by 1.

A table 48 in FIG. 3 shows the encoding of the decimal number0.02813720703125 as an example. The associated bit sequence includes sixleading zeroes. Of these, five zeroes are omitted, and the remainingmantissa (the next 8 digits) is entered in row k=5.

Similarly, for negative numbers the leading ones except for the last maybe omitted. Since for the omitted leading digits, additional leastsignificant bits may be incorporated into the mantissa, higher accuracyin the representation of the real number is achieved in the exponentialrepresentation.

For the case illustrated in table 46, underneath the original decimalnumber 0.840 . . . the value of the decimal number after conversion intothe exponential representation is indicated: 0.8359375. A comparison ofthe two decimal numbers shows that limiting the mantissa to 8 bitsresults in a quantization error in the range of 0.004.

Also for the case illustrated in table 48, the decimal numbers thatcorrespond to the original bit sequence and to the exponentialrepresentation are indicated. It is apparent that the quantization erroris much smaller here due to the scaling by k=5 digits.

In FIG. 4, a table 50 illustrates the encoding in an exponentialrepresentation according to a method according to the present invention,using the same decimal number as in FIG. 3 (table 46) as an example. Thespecial feature of this method is that base b=4 is used, not customarybase b=2. The increase of exponent k by 1 thus corresponds tomultiplying by the factor 2⁻². Accordingly, in table 50 the rows areeach shifted by two digits relative to one another. In order to coverthe same dynamic range as in FIG. 3 (digits from 2⁰ to 2⁻¹⁴), exponentsk in the range of 0 to 3, which may be encoded by a 2-bit word, aresufficient. Length q may thus be reduced from 3 to 2. As a result,either memory space is saved, or the bit that is freed up is utilized toincrease length p of the mantissa from 8 to 9, so that greater accuracyis achieved and the quantization error is reduced.

In table 50 the mantissa has a length of 9 bits, so that of the original11-bit word, only the last two digits need to be discarded. Theassociated decimal numbers are likewise indicated in FIG. 4, and showthat the quantization error has decreased to approximately 0.001.

However, the method applied in this example does not result in areduction in the quantization error for every real number. Acounterexample is shown in FIG. 5. First, a table 52 illustrates theconventional exponential representation with base b=2, p=8, and q=3 foran 11-bit word, which in this example has two leading zeroes. In theconventional method, the leading 0 is deleted and the exponent isincreased to k=1. Thus, of the original 11-bit word, only the last twobits need to be discarded.

A table 54 in FIG. 5 illustrates the method according to the presentinvention for the same 11-bit word, with b=4, p=9, and q=2. If k were tobe increased from 0 to 1, the two leading zeroes would have to bedeleted. However, for the remaining mantissa the most significant bitwould then be a 1, which in two's complement format would correspond toa negative number. Therefore, in table 54 the encoding must take placewith k=0, and the same data loss as in table 52 results, even though themantissa is lengthened to nine digits.

When a plurality of real values is to be encoded, and the magnitudes ofthese values are approximately equally distributed, in approximatelyone-half of the cases the number of leading zeroes will be odd, as inFIG. 4, and a reduction in the quantization error is achieved, while inthe other half of the cases the number of leading zeroes (or ones) willbe even, so that no advantage results over the conventional method.However, on a statistical average, use of the method according to thepresent invention always results in a significant improvement in theaccuracy for one-half of the data.

In FIG. 6, a table 56 illustrates one variant of the method according tothe present invention, with base b=4 and with conventional length p=8 ofthe mantissa and conventional length q=3 of exponent k. Overall, forstoring the mantissa and the exponent this results in the same memoryspace requirements (11 bits) as in FIGS. 3 through 5. Although in thiscase no greater accuracy is achieved by lengthening the mantissa, withthe same 11 bits as in the related art a significantly greater dynamicrange, namely, of 2⁰ to 2⁻²¹, may be covered.

Processing stages 44 in signal processing unit 32 are each designed fora certain task, and the essential features of the data structure of thedata to be processed and to be stored are known in advance. Thus, foreach individual processing stage 44 it may be individually determinedwhich variant of the method according to the present invention should beused. When a large dynamic range is required, q will be increased. Whenthe expected dynamic range is smaller, p may be increased, thusachieving greater accuracy. In certain cases it may also be advantageousto operate with an even larger base, for example b=8; the base shouldpreferably be a power of two.

FIG. 7 illustrates an encoding method according to a second exemplaryembodiment of the present invention. In this exemplary embodiment, kdoes not directly indicate the exponent in the exponentialrepresentation, and instead k is merely the argument of a function f(k),whose function value then determines the exponent. The exponentialrepresentation thus has the form:

r=m*·b ^(f(k)),

where the mantissa is denoted here by m*.

FIG. 7 shows examples of value tables 58, 60, 62, 64, each of whichdefines a different function f. In value tables 58, 60, and 62 theassociation of the function values or of the powers b^(f(k)) formed fromsame is explicitly indicated for arguments k.

The advantage of this method is that, also for a given length q=2 ofargument k to be stored, one is not limited to the four lowest powers4⁰, 4⁻¹, 4⁻², and 4⁻³ (as in value table 58), but instead, some otherset of four powers of four may be selectively used, as shown in theexample in value tables 60 and 62. The selection of function f and ofthe associated value table may then be based on which set of powers bestfits the expected or previously found structure of the data to bestored. This is explained in greater detail below.

The data in this example are stored in memory 40 in various data blocks66, 68, 70, and for each data block an indicator 72 which refers to oneof value tables 58 through 64 is additionally stored. The data in eachdata block are encoded and decoded with function f, which is indicatedby indicator 72.

FIG. 8 shows a data set 74 to be stored, which in this simplifiedexample is made up of only five bit sequences, each having a length of22 bits. However, the dynamic range in this example is only 14 bits,since all least significant bits are 0. The first three bit sequencescorrespond to real numbers in the range 2⁰, while the last two bitsequences indicate smaller numbers in the range of 2⁻⁴ or 2⁻⁶.

In addition, FIG. 8 shows three tables 76, 78, 80, each of whichrepresents the exponential representation with one of functions f shownin FIG. 7. Associated value tables 58, 60, and 62 are likewise indicatedin FIG. 8.

To check how well, for example, the exponential representation accordingto table 76 is suited for data set 74, for each bit sequence in data set74 a row may now be selected from table 76 with which the bits that aredifferent from 0 may be optimally covered. The bits covered in this wayare denoted in data set 74 by a frame 82. It is apparent that the firstbit sequence may be completely covered by row k=0, and the last bitsequence may be completely covered by row k=3. For the three other bitsequences, several least significant bits are lost in each case.

When the same procedure is now repeated with tables 78 and 80, it isapparent that the overall data loss that occurs is greater for thesetables. Therefore, for encoding data set 74, function f that is definedby value table 58 (table 76) would be selected.

Analogously, FIG. 9 shows an example of a data set 84 that may be bestmapped with value table 60 (table 78), and FIG. 10 shows an example of adata set 86 that may be best mapped with value table 62 (table 80).

An error measure, for example the sum of the quantization error, theaverage quadratic deviation, etc., may be computed as a criterion forselecting best suited function f.

FIG. 11 shows a more comprehensive data set 88 that includes a total oftwenty bit sequences. These bit sequences are ordered, at least roughly,in decreasing value of the real numbers that are represented by the bitsequence. This corresponds to a situation that is frequently encounteredin practice. For example, the bit sequences could represent theamplitudes of received radar echoes with increasing frequencies andcorrespondingly increasing object distances. The sorting by decreasingvalues then automatically results due to the fact that the radar echoesbecome weaker with increasing object distance.

To minimize the memory requirements and/or to increase the accuracy, itis now advantageous to divide such an ordered or partially ordered dataset into individual blocks 90, 92, 94, and for each block to selectfunction f that best fits the data structure of this block. For example,if a function f in whose value range low powers of four predominantlyoccur were selected for block 90, while for block 94 a function in whosevalue range predominantly high powers of four predominantly occur wereselected, the leading zeroes or ones occurring in all bit sequences inblock 94 may be scaled off.

When the field of application of the radar sensor is known, theselection of function f or of functions f for various blocks, as well asthe base to be used (p=4 or greater) and length p of the mantissa andlength q of argument k, may be set before initial start-up of the radarsensor. However, in a further embodiment it is also possible todynamically adapt these parameters during operation of the radar sensor,based on the instantaneous data to be processed.

Instead of defining functions f with the aid of predefined and storedvalue tables 58, 60, 62, in a further embodiment it is also possible togenerate function f, to be applied in each case, directly during thedata compression by selecting those powers of four with which thesignificant bits in the bit sequences to be compressed may be bestcovered.

For example, the selection or generation of functions f may take placebased on a statistical analysis in which, based on the bit sequences tobe stored, a histogram is created which for each power e of base bindicates number n of bit sequences whose highest significant bit (afterdeleting the leading ones or zeroes) is in the interval between b^(−e)and b^(−e−1). Examples of such histograms are shown in FIGS. 12 and 13.In FIG. 12, the values of the highest significant bits are either in therange of b⁰ to b⁻¹ or in the range of b⁻⁵ to b⁻⁷. However, since with anargument k of length 2 only four different powers may be indicated,among the powers that occur, if at all, the four lowest powers, in thepresent example b⁰, b⁻¹, b⁻⁵, and b⁻⁶, are selected. Bit sequences whosesignificant bits begin with b⁻⁷ are encoded in the form m·b⁻⁶, for whicha certain data loss must be accepted.

FIG. 13 shows an example in which the highest significant bits areeither in the range of b⁻³ to b⁻⁵ or are b⁻⁹. Therefore, in this casepowers b⁻³, b⁻⁴, b⁻⁵, and b⁻⁹ are selected.

FIG. 14 shows a block diagram of a signal processing unit 32′ in whichthe parameters for the data compression may be dynamically adapted.Inserted between input stage 36 and compression stage 38 is a statisticsmodule 96, which carries out a statistical analysis on the data receivedfrom input stage 36, for example by creating histograms of the typeshown in FIGS. 12 and 13. A subdivision of the data set, to be stored,into blocks having a similar data structure optionally takes place inthis statistics module 96. The results of the statistical analysis forthe complete data set or for the block considered at that moment arethen transferred to a selection module 98, which determines the valuetable for function f to be applied, and optionally optimal parameters pand q and possibly also base b, when these parameters are to be greaterthan 4. The parameters (and functions) determined by selection module 96are transferred to compression stage 38, where they are used for datacompression.

The compressed data, together with the parameters used (or an indicatorfor the parameter set used), are then stored block by block in memory40.

Only the encoding of real numbers is considered in the method describedthus far. However, it is understood that the method may also be appliedto complex numbers, since any complex number may be expressed by tworeal numbers, for example by its real part and its imaginary part, oralso by its magnitude and the phase. The above-described encoding methodmay then be used for encoding each, or at least one, of the two realnumbers that represent the complex number. For example, the exponentialrepresentation may be used for the magnitude, and a fixed-pointrepresentation may be used for the phase. In many applications in aradar sensor, this representation of complex numbers is particularlyadvantageous, since in the data evaluation a phase compensation is oftenrequired, which is simplified to a mere addition of the phases in therepresentation of the complex values by magnitude and phase. Applicationexamples include the phase compensation for a synthetic aperture radar(SAR) or also the phase compensation for radar sensors with OFDMmodulation.

What is claimed is:
 1. A method for encoding and storing digital data,which include a plurality of real values, the method comprising:storing, in a signal processing unit of a radar sensor, each of at leastone real value r in an exponential representation in the formr=m·b^(−k), where m is a digital mantissa having a length p, b is abase, and k is a positive number that is encoded as a digital numberhaving a length q; wherein the exponential representation with b>2 isused for the compressed storage of the at least one value r.
 2. Themethod as recited in claim 1, wherein b is a power of two.
 3. The methodas recited in claim 1, wherein p and q are determined as a function ofan expected data structure of values to be stored.
 4. The method asrecited in claim 3, wherein during operation of the radar sensor, pand/or q and/or b are dynamically adapted to the data structure of thevalues to be stored.
 5. The method as recited in claim 1, wherein forthe compressed storage, each of the at least one value r is transformedinto an exponential representation in the form r=m*·b^(−f(k)), where m*is the mantissa and f is a function of k that is selected from multiplefunctions, and the selection of the function f takes place based on avalue distribution of values to be stored.
 6. The method as recited inclaim 5, wherein the multiple functions from which the function f isselected are stored in advance in the form of value tables.
 7. Themethod as recited in claim 5, wherein the selection of the function f isvaried during operation of the radar sensor as a function of the datastructure of the at least one value to be stored.
 8. The method asrecited in claim 5, wherein values of the selected function f aregenerated during operation of the radar sensor as a function of the datastructure of the at least one value to be stored.
 9. The method asrecited in claim 3, wherein parameters and/or functions that are usedfor the data compression are determined based on a statistical analysisof data to be stored.
 10. The method as recited in claim 1, wherein acomplex number is represented by its magnitude and its phase, and theexponential representation is used for the magnitude.
 11. A radar sensorfor a motor vehicle, comprising: a signal processing unit configured toencode and storing digital data, which include a plurality of realvalues, the signal processing unit configured to: store, in a signalprocessing unit of a radar sensor, each of at least one real value r inan exponential representation in the form r=m·b^(−k), where m is adigital mantissa having a length p, b is a base, and k is a positivenumber that is encoded as a digital number having a length q; whereinthe exponential representation with b>2 is used for the compressedstorage of the at least one value r.